**# playlist of the 46 videos (click the up-left corner of the video)**

source: nptelhrd 2013年7月2日

Mathematics - A Basic Course in Real Analysis by Prof. P. D. Srivastava, Department of Mathematics, IIT Kharagpur. For more details on NPTEL visit http://nptel.iitm.ac.in

Mod-01 Lec-01 Rational Numbers and Rational Cuts 52:37

Mod-02 Lec-02 Irrational numbers, Dedekind's Theorem 54:42

Mod-03 Lec-03 Continuum and Exercises 56:11

Mod-03 Lec-04 Continuum and Exercises (Contd.) 55:00

Mod-04 Lec-05 Cantor's Theory of Irrational Numbers 53:08

Mod-04 Lec-06 Cantor's Theory of Irrational Numbers (Contd.) 55:06

Mod-05 Lec-07 Equivalence of Dedekind and Cantor's Theory 54:37

Mod-06 Lec-08 Finite, Infinite, Countable and Uncountable Sets of Real Numbers 55:18

Mod-07 Lec-09 Types of Sets with Examples, Metric Space 55:02

Mod-08 Lec-10 Various properties of open set, closure of a set 55:20

Mod-09 Lec-11 Ordered set, Least upper bound, greatest lower bound of a set 56:22

Mod-10 Lec-12 Compact Sets and its properties 55:44

Mod-11 Lec-13 Weiersstrass Theorem, Heine Borel Theorem, Connected set 56:08

Mod-12 Lec-14 Tutorial - II 56:13

Mod-13 Lec-15 Concept of limit of a sequence 54:51

Mod-14 Lec-16 Some Important limits, Ratio tests for sequences of Real Numbers 51:48

Mod-15 Lec-17 Cauchy theorems on limit of sequences with examples 54:15

Mod-16 Lec-18 Fundamental theorems on limits, Bolzano-Weiersstrass Theorem 54:36

Mod-17 Lec-19 Theorems on Convergent and divergent sequences 52:42

Mod-18 Lec-20 Cauchy sequence and its properties 53:53

Mod-19 Lec-21 Infinite series of real numbers 53:16

Mod-20 Lec-22 Comparison tests for series, Absolutely convergent and Conditional convergent series 54:53

Mod-21 Lec-23 Tests for absolutely convergent series 53:01

Mod-22 Lec-24 Raabe's test, limit of functions, Cluster point 57:20

Mod-23 Lec-25 Some results on limit of functions 53:36

Mod-24 Lec-26 Limit Theorems for functions 54:09

Mod-25 Lec-27 Extension of limit concept (one sided limits) 52:26

Mod-26 Lec-28 Continuity of Functions 54:22

Mod-27 Lec-29 Properties of Continuous Functions 54:07

Mod-28 Lec-30 Boundedness Theorem, Max-Min Theorem and Bolzano's theorem 56:25

Mod-29 Lec-31 Uniform Continuity and Absolute Continuity 53:41

Mod-30 Lec-32 Types of Discontinuities, Continuity and Compactness 55:55

Mod-31 Lec-33 Continuity and Compactness (Contd.), Connectedness 55:59

Mod-32 Lec-34 Differentiability of real valued function, Mean Value Theorem 53:52

Mod-33 Lec-35 Mean Value Theorem (Contd.) 56:46

Mod-34 Lec-36 Application of MVT , Darboux Theorem, L Hospital Rule 52:54

Mod-35 Lec-37 L'Hospital Rule and Taylor's Theorem 54:06

Mod-36 Lec-38 Tutorial - III 52:42

Mod-37 Lec-39 Riemann/Riemann Stieltjes Integral 53:03

Mod-38 Lec-40 Existence of Reimann Stieltjes Integral 55:39

Mod-39 Lec-41 Properties of Reimann Stieltjes Integral 54:35

Mod-39 Lec-42 Properties of Reimann Stieltjes Integral (Contd.) 56:45

Mod-40 Lec-43 Definite and Indefinite Integral 55:39

Mod-41 Lec-44 Fundamental Theorems of Integral Calculus 52:12

Mod-42 Lec-45 Improper Integrals 55:53

Mod-43 Lec-46 Convergence Test for Improper Integrals 53:47

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